On the Solutions of Four Second-Order Nonlinear Difference Equations

Periodic Solutions of Second Order Nonlinear Functional Difference Equations

The development of the study of periodic solution of functional difference equations is relatively rapid. There has been many approaches to study periodic solutions of difference equations, such as critical point theory, fixed point theorems in Banach spaces or in cones of Banach spaces, coincidence degree theory, KaplanYorke method, and so on, one may see [3-7,11,13-15] and the references ther...

Periodic solutions for nonlinear second-order difference equations

We establish conditions for the existence of periodic solutions of nonlinear, second-order difference equations of the form y(t + 2) + by(t + 1) + cy(t) = f (y(t)), where c = 0 and f :R→ R is continuous. In our main result we assume that f exhibits sublinear growth and that there is a constant β > 0 such that u f (u) > 0 whenever |u| ≥ β. For such an equation we prove that ifN is an odd integer...

Nontrivial Periodic Solutions for Nonlinear Second-Order Difference Equations

On a System of Second-Order Nonlinear Difference Equations

This paper is concerned with dynamics of the solution to the system of two second-order nonlinear difference equations 1 1 1 n n n n x x A x y + − − = + , 1 1 1 n n n n y y A x y + − − = + ,  n = 0,1, , where ( ) 0, A∈ ∞ , ( ) 0, i x− ∈ ∞ , ( ) 0, i y− ∈ ∞ , i = 0, 1. Moreover, the rate of convergence of a solution that converges to the equilibrium of the system is discussed. Finally, some num...

Uncountably many bounded positive solutions for a second order nonlinear neutral delay partial difference equation

In this paper we consider the second order nonlinear neutral delay partial difference equation $Delta_nDelta_mbig(x_{m,n}+a_{m,n}x_{m-k,n-l}big)+ fbig(m,n,x_{m-tau,n-sigma}big)=b_{m,n}, mgeq m_{0},, ngeq n_{0}.$Under suitable conditions, by making use of the Banach fixed point theorem, we show the existence of uncountably many bounded positive solutions for the above partial difference equation...